SOLUTION: If {{{ 2−x^2 }}} ≤ {{{ g(x) }}} ≤ {{{ 2cos(x) }}} for all x, find lim(x→0) {{{ g(x) }}}

SOLUTION: If {{{ 2−x^2 }}} ≤ {{{ g(x) }}} ≤ {{{ 2cos(x) }}} for all x, find lim(x→0) {{{ g(x) }}}

Algebra.Com

Question 1013489: If ≤ ≤ for all x, find lim(x→0)
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Since cos(x) cannot be greater than 1, it appears that for
2 <= g(x) <= 2cos(x)
yields
1 <= (1/2)g(x) <= cos(x)
and cos(x) = (1/2)g(x) = 1
Now cos(0) = 1.
Therefore it appears g(0) = 2.
RELATED QUESTIONS
Given that −x^2−2x−4 ≤ f(x) ≤ x^2+2x−2 for all x,... (answered by solver91311)

Consider f(x) = {x^2−1, x < 1 f(x) = {0, 1 < x ≤ 3 f(x) =... (answered by solver91311)

Find lim x→−1 for 2x^3 − 5x (answered by Fombitz)

Please help me solve these functions: Find formulas for (f o g)(x) if f(x)= {1, if (answered by rothauserc)

Solve |x − 2| ≤ 5. (answered by rothauserc)

6. Let f = { | 4 − x^2 if x ≤ 2 | x^3 − 2x^2 + a, if x > 2 {... (answered by stanbon)

Suppose that the function g is defined on the interval [-2,2) as follows g(x)= -2 (answered by Fombitz)

Find lim 2x3 − 5x. x→−1 (answered by Alan3354,ikleyn)

lim g(x)=x^2-4/x+2... (answered by ikleyn)